1. Two individuals invest in a project which takes two periods to complete. At the start of period one, person A invests 4.5 and person B invests 1.5. At the end of period one, each of the investors has achance to withdraw her investment.

The decisions whether to withdraw from the project or not are madesimultaneously. If either investor withdraws, the project is scrapped and the scrapped value is 4. If both investors withdraw, they share the scrapped value in proportion to their investment; A gets 3 and B gets1.

If one investor withdraws while the other does not, the one who withdraws gets the first claim on the scrapped value up to the amount of her investment;

if A withdraws while B does not, A gets min(4.5, 4)and B gets 4 - min(4.5, 4).

If B withdraws while A does not, B gets min(1.5, 4) and A gets the rest of thescrapped value.

If neither investor withdraws at the end of period one, the investors have another chanceto withdraw at the end of period two.

If either investor withdraws, the payoffs are the same as before.

If neither investor withdraws at the end of period two, the project is completed and the investors get the total of 12 in gross return which they share in proportion to their original investment. There is no discounting.

a. Draw the extensive form of the above game.

b. How many pure strategies are there for investor A? How many for investor B?Give an example of a pure strategy for each investor.

c. What are the pure strategy subgame perfect Nash equilibria? Explain your answer.

d. Interpret the answer to c. Is there any problem with treating subgame perfect Nash equilibrium as aprediction of the outcome of rational play in this game?